The beauty of the Canvass Retractible Roof System is that you have control
over direct solar energy absorbtion.

In the Winter, you keep the retractible, insulated double roof open stacked in its own accordian (is it right to say faberge?) style during the warming sunlight. At night you push the button to close the roof which will help to keep the solar gain in.

In the Summer, you close the retractible, insulated double roof during the daylight. The insulated canvas will absorb all of the solar heat & you have the option of venting the transfere through the side walls of the semicircular roof structure. At night during the summer, you push the button to open the roof & allow heat radiation to escape back into the sky.

//(is it right to say faberge?)// It certainly isn't offensive for you to say "faberge", but assuming you meant the legendary Russian goldsmith and jeweler, it is difficult to understand what this idea might share in common with his ornate gold and enamel creations.

It's just a wild guess, but are you describing a multi-panel "nested shutter" device conceptually similar to the ones occasionally used in smaller observatories?

I did attach a link on the off chance that this helps illustrate your idea. I'll remove it if you come up with a better way to describe your idea that doesn't sound like a lot of other products already on the market, or it becomes clear that everyone else is clearly understanding what I'm struggling to visualize.

The shadecloth could simply
retract into the roof cavity
under the ridge. This is the
aesthetically pleasing, town
planning friendly version. No
big ugly boxes or lumpy canvas
stacks added to your roof, just a
subtle slit along either side of
the ridge line. Each edge of the
slit is a roller. The retraction
mechanism is also inside the
roof. I'm picturing more like a
roll-up window blind/projector
screen.

The bottom (eaves end when
extended) edge of the canvas
would be attached to a bracing
rod. This is shaped to fill in and
cap the slit, and coloured to
match your existing roofing.

In fact, pull it all the way in
under the roof, and presto,
extra winter insulation.
Summer position, above roof,
reflective side facing up. Winter
position, below roof, reflective
side facing down to keep the
heat in.

A reflective surface would be
more effective than canvas, and
cheaper than insulated canvas.
You want that summer heat
bouncing away.

An air gap integrated into the
re-engineered ridge line would
allow any hot air generated in
the roof-shadecloth interstice to
thermosiphon away.